Question

Engida Tz has estimated the following demand relationship for its product over the last four years, using monthly
observations:

lnQ_t = 4.932 -1.238lnP_t+ 1.524lnY_t-1+ 0.4865lnQ_t-1

(2.54) (1.38) (3.65) (2.87)

_R²_{= 0.8738}

Q = sales in units, P = price in $, and Y is income in $,000

a.Make a sales forecast if price is $12, income last month was $30,000 and sales last month were 2,980 units

b. Make a sales forecast for the following month if there is no change in price or income
c. If price is increased by 7 per cent in general terms, estimate the effect on sales, stating any assumptions.

Answer 1

(a) The estimated regression model is . For the given values, we have or or or units.

Note that we have putted Y=30, since Y is in thousands, ie putting Y=30 corresponds to Y=30 thousand dollars.

(b) For no change in price and income, we have the forecast as , ie or or or units, which is the following month's forecast of sales.

(c) For , we have or or , ie or , which is the price elasticity of demand. This means that for a unit percent increase in price, the demand would decrease by 1.238%.

Hence, we have , and for increase in price by 7%, we have or or . This means that for an increase in price by 7%, the demand decreases by 8.666%.

The assumption is that this is more general estimate of the change in sales, and to get a more specifit estimate, previous month's sales must be a given.